Integrated control of active tire steer and brakes

ABSTRACT

An integrated active steering and braking control system for providing one or more corrective yaw moments to a vehicle in response to a plurality of signals indicative of operational and environmental conditions related to the vehicle is disclosed. The system comprises a reference model, an estimator, a vehicle level brake/steer controller, and an actuator controller. The reference model provides a feedforward front steering angle correction signal a feedforward rear steering angle correction signal, a desired yaw rate signal, a desired lateral velocity signal, and a desired side slip angle signal. The estimator provides an estimated surface coefficient of adhesion signal, an estimated lateral velocity signal, and an estimated side slip angle signal. In response to the signals from the reference model and the estimator, the vehicle level brake/steer controller provides either a desired speed differential signal, a desired front steering angle signal and/or a desired rear steering angle signal. The actuator controller selectively provides a corrective braking signal to a brake actuator, a corrective front steering signal to a steering actuator, and a corrective rear steering signal to the steering actuator as a function of the desired speed differential signal, the desired front steering angle signal, and the desired rear steering angle signal, respectively.

FIELD OF THE INVENTION

[0001] The present invention generally relates to control systems forautomotive vehicles, and more particularly relates to an integratedcontrol of an active steering system and a brake system of an automotivevehicle for improving upon a handling, stability, and a maneuverabilityof the automotive vehicle.

BACKGROUND OF THE INVENTION

[0002] Some automotive vehicles known in the art utilize an active brakecontrol to enhance a directional stability of the vehicle at or close toa limit of adhesion. Some other automotive vehicles known in the artutilize a limited active control of a rear tire steering angle in orderto improve a vehicle handling and maneuverability at low speeds. Morerecently, automotive vehicles are utilizing a limited active control ofa front tire steering angle to introduce a steering correction to asteering angle commanded by a vehicle driver in an effort to improve avehicle directional stability. The present invention addresses a needfor an integrated control of vehicle brakes, and a front tire steeringangle and/or a rear tire steering angle.

SUMMARY OF THE INVENTION

[0003] One form of the present invention is an integrated activesteering and braking control method for a vehicle. First, a firstcorrective yaw moment for the vehicle as a function of a steering angleof an axle of the vehicle is determined, and a second corrective yawmoment for the vehicle as a function of a speed differential between afirst tire and a second tire of the vehicle is determined. Second, acorrective steering signal is provided to a steering system of thevehicle whereby the first corrective yaw moment is applied to thevehicle, and a corrective braking signal is provided to a braking systemof the vehicle whereby the second corrective yaw moment is applied tothe vehicle.

[0004] A second form of the present invention is also an integratedactive steering and braking control method for a vehicle. First, adesired speed differential between the speed of the first tire and thespeed of the second tire is determined. Second, a desired steering angleof the axle as a function of said desired speed differential isdetermined.

[0005] A third form of the present invention is also an integratedactive steering and braking control method for a vehicle. First, afeedforward portion of a corrective front steering angle signal inresponse to a plurality of operational signals indicative of anoperational state of the vehicle is determined. Second, a feedforwardportion of a corrective rear steering angle signal in response to saidplurality of operational signals.

[0006] A fourth form of the present invention is also an integratedactive steering and braking control system for a vehicle comprising afirst controller and a second controller. The first controller isoperable to determine a first corrective yaw moment for the vehicle as afunction of a steering angle of an axle of the vehicle, and to determinea second corrective yaw moment for the vehicle as a function of a speeddifferential between a first tire and a second tire of the vehicle. Thesecond controller is operable to provide a corrective steering signal toa steering system of the vehicle whereby the first corrective yaw momentis applied to the vehicle, and to provide a corrective braking signal toa braking system of the vehicle whereby the second corrective yaw momentis applied to the vehicle.

[0007] A fifth form of the present invention is also an integratedactive steering and braking control system for a vehicle. The systemcomprises a means for determining a feedforward portion of a correctivefront steering angle signal in response to a plurality of operationalsignals indicative of an operational state of the vehicle. The systemfurther comprises a means for determining a feedforward portion of acorrective rear steering angle signal in response to said plurality ofoperational signals.

[0008] A sixth form of the present invention is a vehicle comprising anaxle, a first tire, a second tire, and an integrated active steering andbraking control system. The system is operable to determine a desiredspeed differential between a speed of the first tire and a speed of thesecond tire and to determine a desired steering angle of the axle as afunction of the desired speed differential.

[0009] The foregoing forms, and other forms, features and advantages ofthe present invention will become further apparent from the followingdetailed description of the presently preferred embodiments, read inconjunction with the accompanying drawings. The detailed description anddrawings are merely illustrative of the present invention rather thanlimiting, the scope of the present invention being defined by theappended claims and equivalents thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

[0010]FIG. 1A is a vector diagram illustrating a yaw moment of a vehiclethat is generated by a differential braking of a pair of front tires ofthe vehicle as known in the art;

[0011]FIG. 1B is a vector diagram illustrating a yaw moment of a vehiclethat is generated by a front tire steering of the vehicle as known inthe art;

[0012]FIG. 1C is a vector diagram illustrating a yaw moment of a vehiclethat is generated by a differential braking of a pair of rear tires ofthe vehicle as known in the art;

[0013]FIG. 1D is a vector diagram illustrating a yaw moment of a vehiclethat is generated by a rear tire steering of the vehicle as known in theart;

[0014]FIG. 2 is a block diagram of one embodiment of a coordinatedcontrol system in accordance with the present invention;

[0015]FIG. 3 is a block diagram of one embodiment of a vehicle referencemodel of FIG. 2 in accordance with the present invention;

[0016]FIG. 4 is a graph illustrating three (3) feedforward gain curvesfor an active rear steer as a function of a vehicle speed in accordancewith the present invention;

[0017]FIG. 5 is a block diagram of one embodiment of a surfacecoefficient estimator in accordance with the present invention;

[0018]FIG. 6 is a block diagram of one embodiment of a side slipvelocity estimator in accordance with the present invention;

[0019]FIG. 7 is a block diagram of one embodiment of a vehicle levelbrake/steer controller in accordance with the present invention; and

[0020]FIG. 8 is a graph of a lateral tire force vs. a tire slip angle inaccordance with the present invention.

DETAILED DESCRIPTION OF THE PRESENTLY PREFERRED EMBODIMENTS

[0021] Referring to FIGS. 1A-1D, a vehicle 10 including a front axle 11having a front left tire 12 and a front right tire 13 coupled thereto,and a rear axle 14 having a rear left tire 15 and a rear right tire 16coupled thereto is shown. As known by those having ordinary skill in theart, a response of vehicle 10 in a yaw plane is primarily dictated by acombination of longitudinal tire forces and lateral tire forces beingapplied to tires 11, 12, 15, and 16. Good handling of vehicle 10 in theyaw plane requires that a yaw rate (i.e. a rate of rotation of vehicle10 about a vertical axis 17 passing through the center of gravity ofvehicle 10) and a lateral acceleration of vehicle 10 be consistent withdriver intentions, subject to a physical limit imposed by a surfacecoefficient of adhesion. Since the vehicle yaw rate is determined by ayaw moment acting on vehicle 10 (i.e. a moment of forces about verticalaxis 17), a main mechanism to control vehicle yaw response is bygenerating a corrective yaw moment. This can be achieved by applying oneor more brakes (not shown) to tires 11, 12, 15, and/or 16; by a changein a steering angle of front axle 11; or by a change in a steering angleof rear axle 14.

[0022] For example, when vehicle 10 is being driven straight asillustrated in FIG. 1A, a brake force F_(x) can be applied to frontright tire 13 to generate corrective yaw moment ΔM_(z1) in a clockwisedirection about vertical axis 17. Corrective yaw moment ΔM_(z1) can becomputed by the following equation (1):

ΔM _(z1) =F _(x)*(t _(w)/2)  (1)

[0023] where t_(w) is a track width. In a linear range of tireoperation, brake force F_(x) can be approximated by the followingequation (2):

F _(x) =C _(x) *λ=C _(x)*(Δv_(lr1) /v)  (2)

[0024] where C_(x) is a tire longitudinal stiffness; λ is a brake slip;Δv_(lr1) is a difference in a linear speed of tire 12 and a linear speedof tire 13; and v is a vehicle speed of vehicle 10. Combining equations(1) and (2) yields the following equation (3):

ΔM _(z1) =C _(x)*(t _(w)/2)*Δv_(lr1) /v  (3)

[0025] As illustrated in FIG. 1B, tire 12 and tire 13 can also becontrolled to generate corrective yaw moment ΔM_(z2) as a function ofincremental front steering angle Δδ_(f). Corrective yaw moment ΔM_(z2)can be computed by the following equation (4):

ΔM _(z2) =F _(y1) *a  (4)

[0026] where a is the distance from axis 17 to front axle 11; and F_(y1)is the total lateral force on both tire 12 and tire 13, which in thelinear range of tire operation can be computed by the following equation(5):

F _(y1)=2*C _(y)*Δδ_(f)  (5)

[0027] where C_(y) is a cornering stiffness coefficient of both tire 12and tire 13. Thus, corrective yaw moment ΔM_(z2) can also be computed bythe following equation (6):

ΔM _(z2)=2*C _(y) *a*Δδ _(f)  (6)

[0028] Equating yaw moment ΔM_(z2) to yaw moment ΔM_(z1) can beaccomplished by computing front steering angle Δδ_(f) under thefollowing equation (7) with the assumption that tire longitudinalstiffness coefficient C_(x) and tire lateral stiffness C_(y) areapproximately equal:

Δδ_(f)=(C _(x) *t _(w)/(4*C _(y) *a))*(ΔV _(lr1) /v)≈[t _(w)/(4*a)]*(ΔV_(lr1) /v)  (7)

[0029] Also by example, when vehicle 10 is being driven straight asillustrated in FIG. 1C, brake force F_(x) can be applied to rear righttire 16 to generate corrective yaw moment ΔM_(z3) in a clockwisedirection about vertical axis 17. Corrective yaw moment ΔM_(z3) can becomputed by equation (1). In a linear range of tire operation, brakeforce F_(x) can be approximated by the following equation (8):

F _(x) =C _(x) λ*=C _(x)*(ΔV _(lr2) /v)  (8)

[0030] where C_(x) is a tire longitudinal stiffness; λ is a brake slip;ΔV_(lr2) is a difference in a linear speed of tire 15 and a linear speedof tire 16; and v is a vehicle speed of vehicle 10. Combining equations(1) and (8) yields the following equation (9):

ΔM _(z3) =C _(x)*(t _(w)/2)*ΔV _(lr2) /v  (9)

[0031] As illustrated in FIG. 1D, tire 15 and tire 16 can also becontrolled to generate corrective yaw moment ΔM_(z4) as a function ofincremental rear steering angle Δδ_(r). Corrective yaw moment ΔM_(z4)can be computed by the following equation (10):

ΔM _(z4) =F _(y2) *b  (10)

[0032] where b is the distance from axis 17 to rear axle 14; and F_(y2)is the total lateral force on both tire 15 and tire 16, which in thelinear range of tire operation can be computed by the following equation(11):

F _(y2)=−2*C _(y) *Δδr  (11)

[0033] where C_(y1) is a cornering stiffness coefficient of both tire 15and tire 16. Thus, corrective yaw moment ΔM_(z4) can also be computed bythe following equation (12):

ΔM _(z4)=−2*C _(y) *a*Δδ _(r)  (12)

[0034] Equating yaw moment ΔM_(z4) to yaw moment ΔM_(z3) can beaccomplished by computing rear steering angle Δδ_(r) under the followingequation (13) with the assumption that tire longitudinal stiffnesscoefficient C_(x) and tire lateral stiffness C_(y) are approximatelyequal:

Δδ_(r) =−[C _(x) *t _(w)/(4*C _(y) *b)]*(Δv _(lr2) /v)≈−[t_(w)/(4*b)]*(Δv _(lr2) /v)  (13)

[0035] The present invention is an integrated active steering andbraking control method based on equations (7) and (13) that selectivelyutilizes tire speed differential signal ΔV_(lr1) to generate correctiveyaw moment ΔM_(z1) and/or to generate corrective yaw moment ΔM_(z2) whenvehicle 10 has an active front steering system, and selectively utilizestire speed differential signal ΔV_(lr2) to generate corrective yawmoment ΔM_(Z3) and/or corrective moment ΔM_(z4) when vehicle 10 has anactive rear steering system.

[0036] Referring to FIG. 2, an integrated active steering and brakingcontrol system 11 for vehicle 10 in accordance with the presentinvention is shown. System 11 comprises a reference model 20, anestimator 30, a vehicle level brake/steer controller 40, and an actuatorcontroller 50. To implement the principals of the present invention,reference model 20, estimator 30, vehicle level brake/steer controller40, and an actuator controller 50 may include digital circuitry, analogcircuitry, or any combination of digital circuitry and analog circuitry.Also, reference model 20, estimator 30, vehicle level brake/steercontroller 40, and an actuator controller 50 may be programmable, adedicated state machine, or a hybrid combination of programmable anddedicated hardware. Additionally, reference model 20, estimator 30,vehicle level brake/steer controller 40, and an actuator controller 50may include any control clocks, interfaces, signal conditioners,filters, Analog-to-Digital (A/D) converters, Digital-to-Analog (D/A)converters, communication ports, or other types of operators as wouldoccur to those having ordinary skill in the art to implement theprincipals of the present invention.

[0037] System 11 is incorporated within a processing environment ofvehicle 10. However, for the simplicity in describing the presentinvention, system 11 is illustrated and described as being separate fromthe processing environment of vehicle 10. Also, for the simplicity indescribing the present invention, system 11 will be described herein asif vehicle 10 includes both a front active braking system and a rearactive steering system. However, those having ordinary skill in the artwill appreciate an applicability of system 11 to a vehicle includingonly a front active braking system or a rear active steering system.

[0038] As known by those having ordinary skill in the art, conventionalsensors (not shown) provide a plurality of signals indicative of anoperational state of vehicle 10 including, but not limited to, a driversteering wheel angle signal δ_(SWA), a front steering wheel angle signalδ_(f), a rear steering wheel angle signal δ_(r), a vehicle yaw ratesignal Ω, a lateral acceleration signal a_(y), a wheel speed signalW_(S1) (from tire 12), a wheel speed signal W_(S2) (from tire 13), awheel speed signal W_(S3) (from tire 15), a wheel speed signs WS_(S4)(from tire 16), and an estimated vehicle speed signal V_(x).

[0039] Reference model 20 inputs driver steering wheel angle signalδ_(SWA), lateral acceleration signal a_(y), and estimated vehicle speedsignal v_(x) from vehicle 10. Alternative to lateral acceleration signala_(y), reference model 20 can input an estimated surface coefficient ofadhesion signal μ_(e) from estimator 30. In response to the inputtedsignals, reference model 20 provides signals indicative of a feedforwardfront steering angle correction signal δ_(fdrl), a feedforward rearsteering angle correction signal δ_(rff), a desired yaw rate signalΩ_(dl), a desired lateral velocity signal v_(yd), and a desired slipangle signal β_(d).

[0040] Estimator 30 inputs front steering wheel angle signal δ_(f), rearsteering wheel angle signal δ_(r), vehicle yaw rate signal Ω, lateralacceleration signal a_(y), and estimated vehicle speed signal v_(x) fromvehicle 10. Estimator 30 further inputs desired yaw rate signal Ω_(dl)from reference model 20. In response to the inputted signals, estimator30 provides an estimated surface coefficient of adhesion signal μ_(e),an estimated lateral velocity signal V_(ye), and an estimated slip anglesignal β_(e).

[0041] Vehicle level brake/steer controller 40 inputs front steeringwheel angle signal δ_(f), rear steering wheel angle signal δ_(r),vehicle yaw rate signal Ω, lateral acceleration signal a_(y) andestimated vehicle speed signal v_(x) from vehicle 10. Controller 40further inputs desired yaw rate signal Ω_(d), desired lateral velocitysignal v_(yd), and desired slip angle signal β_(e) from reference model20; and estimated surface coefficient of adhesion signal lie, estimatedlateral velocity signal v_(ye), and estimated slip angle signal β_(e)from estimator 30. In response to the inputted signals, controller 40provides a desired speed differential signal Δv_(lr3t) indicating adesired speed difference between a linear speed of tire 12 and a linearspeed of tire 13 (FIGS. 1A-1D) or a desired speed difference between alinear speed of tire 15 and a linear speed of tire 16 (FIGS. 1A-1D).Controller 40 further provides a desired front steering angle signalδ_(ftd1) indicative of a desired steering angle of front axle 11 (FIGS.1A-1D), and a desired rear steering angle signal δ_(rtd1) indicative ofa desired steering angle of rear axle 14 (FIGS. 1A-1D).

[0042] Controller 40 only provides desired speed differential signalΔv_(lr3t) and desired front steering angle δ_(ftd1) for alternativeembodiments of vehicle 10 only having a front active steering system.

[0043] Actuator controller 50 inputs desired speed differential signalΔv_(lr3t), desired front steering angle signal δ_(ftd1), and desiredrear steering angle signal δ_(rtd1) from controller 40. Controller 50further inputs front steering wheel angle signal δ_(f), rear steeringwheel angle signal δ_(r), wheel speed signal W_(S1), wheel speed signalW_(S2), wheel speed signal W_(S3), and wheel speed signal W_(S4) fromvehicle 10. In response to the inputted signals, actuator controller 50compares desired tire speed differential signal Δv_(lr3t) to either aspeed differential between tire 12 and tire 13 (FIGS. 1A-1D) asindicated by wheel speed signs WS_(S1) and wheel speed signs WS_(S2) aswould occur to those having ordinary skill in the art, or a speeddifferential between tire 15 and tire 16 (FIGS. 1A-1D) as indicated bywheel speed signs WS_(S3) and wheel speed signs WS_(S4) as would occurto those having ordinary skill in the art. The result is a correctivebraking signal T_(b) that is provided to a braking system (not shown) ofvehicle 10. In one embodiment of vehicle 10, a brake actuator of thebraking system appropriately adjusts brake pressure to a correspondingbrake in response to corrective braking signal T_(b) as would occur tothose having ordinary skill in the art.

[0044] Actuator controller 50 compares desired front steering anglesignal δ_(ftd1) and front steering wheel angle signal δ_(f) as wouldoccur to those with ordinary skill in the art, and compares desired rearsteering angle signal δ_(rtd1) and rear steering wheel angle signalδ_(r) as would occur to those with ordinary skill in the art to therebyprovide a corrective front steering signal T_(fs) and a corrective rearsteering signal T_(rs) to a steering system (not shown) of vehicle 10.In one embodiment of vehicle 10, a front steering actuator of thesteering system adjusts a position of a steering rack for axle 11 (FIGS.1A-1D) in response to corrective front steering signal T_(fs) and a rearsteering actuator of the steering system adjusts a position of asteering rack for axle 14 (FIGS. 1A-1D) in response to corrective rearsteering signal T_(rs).

[0045] Referring to FIG. 3, one embodiment of reference model 20 inaccordance with the present invention is shown. A block 21 convertssteering wheel angle signal δ_(SWA) into a corresponding angle of fronttires signal δ_(fdr) as computed by the following equation (14):

δ_(fdr)=δ_(SWA) * K _(f)(v _(x))  (14)

[0046] where K_(f)(v_(x)) is a ratio between the angle of rotation of asteering wheel of vehicle 10 (FIGS. 1A-1D) and front wheels 12 and 13(FIGS. 1A-1D). In the case of active front steer, front ratioK_(f)(v_(x)) may be speed dependent, for example decreasing with speedto promote maneuverability at low speeds and stability at high speeds.

[0047] A block 22 determines a feedforward part of a steering anglecorrection by limiting a magnitude of front tire steering angle δ_(fdr)to a reasonable level. A desired value of lateral acceleration iscomputed from the following equation (15):

a _(yd)=(v _(x) ²*δ_(fdr))/(L+K _(u) * v _(x) ²)  (15)

[0048] where L is a vehicle tirebase and K_(u) is an understeercoefficient. It follows from equation (15) that in order to limit amagnitude of this acceleration to a reasonable level a_(ydmax) (anexample value of a_(ydmax) is 12 m/s²), a magnitude of steering angleδ_(fdr) has to be limited in accordance with the following equation(16):

[δ_(fmax)]=[a_(ydmax)]*(L+K _(u) *v _(x) ²)/v _(x) ²  (16)

[0049] This limiting can be interpreted as adding a feedforward term tothe steering angle δ_(fff), as given by the following equation (17):$\begin{matrix}{\delta_{fff} = \left\{ \begin{matrix}{\quad 0} & {{{if}\quad {\delta_{fdr}}} \leq {\delta_{f\quad \max}\left( v_{x} \right)}} \\\quad & \quad \\\left\lbrack {{\delta_{f\quad \max}\left( v_{x} \right)} - {{\delta_{fdr}}*{{sign}\left( \delta_{fdr} \right)}}} \right. & {{{if}\quad {\delta_{fdr}}} > {\delta_{f\quad \max}\left( v_{x} \right)}}\end{matrix} \right.} & (17)\end{matrix}$

[0050] After the limitation, front steering angle δ_(fdrl) desired bythe driver is computed from the following equation (18):

δ_(fdrl)=δ_(fdr)+δ_(fff)  (18)

[0051] When vehicle 10 is equipped with a traditional steeringmechanism, the ratio K_(f) does not depend on speed of vehicle 10 andthe limitation of the steering angle cannot be performed, (i.e.δ_(fdrl)=δ_(fdr)).

[0052] A block 23 determines a feedforward part of the rear tiresteering angle δ_(rff) as computed from the following equation (19):

δ_(rff)=δ_(fdr) * K _(rff)(v _(x))  (19)

[0053] where K_(rff)(V_(x)) is a speed dependant gain that must beselected to achieve an improved maneuverability (to reduce radius ofcurvature and/or driver steering effort) at low speeds, an improvedstability at high speeds and a reduction of vehicle side slip velocity(or side slip angle). One possible choice is requiring that the sideslip velocity be equal to zero in a steady state maneuver. Side slipvelocity v_(yss) is computed by the following equation (20):

v _(yss)=[(v _(x)*δ_(fdrl))/(L+K _(u) * v _(x) ²)]*{b−M*a*v _(x) ²/(C_(r) *L)+K _(rff)(v _(x))*[a+M*b*v _(x) ²/(C _(f) *L)]}  (20)

[0054] where M is mass of vehicle 10, a and b are a distances ofvertical axis 17 to front axle 11 and rear axle 14 (FIGS. 1A-1D),respectively, and C_(f) and C_(r) are the cornering stiffnesscoefficients of front tires 12 and 13, and rear tires 15 and 16 (FIGS.1A-1D), respectively. In order to make side slip velocity v_(yss) equalzero, a feedforward gain K_(rff)′(v_(x)) is computed by the followingequation (21):

K _(rff)′(v _(x))=−[b−M*a*v _(x) ²/(C _(r) *L)]/[a+M*b*v _(x) ²/(C _(r)*L)]  (21)

[0055] Feedforward gain K_(rff)′(v_(x)) is illustrated in FIG. 4 ascurve 1. Gain K_(rff)′(v_(x)) is negative for small speeds and positivefor large speeds and it changes sign at a velocity v_(xc) given by thefollowing equation (22):

v _(xc) =[C _(r) *L*b/(M*a)]^(½)  (22)

[0056] Thus, the sign of the rear tire steering angle δ_(rff) isopposite to that of the front steering angle δ_(fdrl) (out of phasesteering) at low speeds, which improves maneuverability. At high speeds,rear tires 15 and 16 are steered in phase with the front tires 12 and13, which improves stability of vehicle 10. In practice, feedforwardgain K_(rff)′(v_(x)) given by equation (21) would require too large reartire steering angle δ_(rff), which is typically limited to severaldegrees. Also, yaw rate Ω of vehicle 10 during cornering maneuvers wouldbe very limited at high velocities, thus compromising subjectivehandling feel. To rectify these problems, feedforward gain K_(rff′(v)_(x)) can be multiplied by a factor η, which is less than 1 inaccordance with the following equation (23):

K _(rff)″(v _(x))=−η*[b−M*a*v _(x) ²/(C _(r) *L)]/[a+M*b*v _(x) ²/(C_(f) *L)]  (23)

[0057] with a reasonable value of η=0.4 (the optimal value for a givenapplication depends on the range of steering angle for rear tires 15 and16). Gain K_(rff)″(v_(x)) given by equation (23) is represented by curve2 in FIG. 4.

[0058] According to equation (22), a velocity v_(xc) at which gainK_(rff) changes sign depends on cornering stiffness C_(r) of rear tires15 and 16. On slippery surfaces, the value of the cornering stiffnessC_(r), and the characteristic velocity v_(xc) (at which gain K_(rff)crosses zero) will be reduced. If the gain determined by equation (23)with the nominal values of cornering stiffness coefficient C_(r) thatcorrespond to a dry surface are used, vehicle 10 will exhibit a tendencyto oversteer during driving on slippery surfaces at the velocities justbelow v_(xc). This is due to out of phase steering increasing a rate ofrotation of vehicle 10. To rectify this problem and make the behavior ofvehicle 10 acceptable over the entire range of surfaces, the feedforwardgain K_(rff) is chosen to be 0 for speed between approximately0.4*v_(xc) and v_(xc), as illustrated by curve 3 in FIG. 4.

[0059] A block 24 determines a steady state desired values of yaw rateΩ_(dss) and side slip velocity v_(ydss). These values can be computedfrom look up tables, which are obtained from vehicle testing performedon dry surface. During tests, the feedforward portion of the rear tiresteering angle δ_(rff) must be active and vehicle 10 must be inapproximately steady state cornering conditions. Thus, the desiredvalues at a given speed and front steering angle δ_(f) represent thevalues which vehicle 10 achieves on dry surface in steady statecornering with the feedforward portion of the rear tire steer beingactive. Another way of obtaining the desired values is by usinganalytical models. For example, the steady state values of yaw rateΩ_(dss) and side slip velocity v_(ydss) can be computed from thefollowing equations (24) and (25):

Ω_(dss)=[1−K _(rff)(v _(x))]*v _(x)*δ_(fdrl) /[L+K _(u) *v _(x) ²]  (24)

v _(ydss)=[(v _(x)*δ_(fdrl))/(L+K _(u) * v _(x) ²)]*{b−M*a*v _(x) ²/(C_(r) *L)+K _(rff)(v _(x))*[a+M*b*v _(x) ²/(C _(f) *L)]}  (25)

[0060] In the equations (24) and (25), an understeer coefficient K_(u)depends on the magnitude of lateral acceleration a_(y). When vehicle 10is without active rear tire steer, feedforward gain K_(rff)=0. Since yawrate Ω and side slip velocity v_(y) are overestimated at large steeringangles by equations (24) and (25), the desired values obtained fromequations (24) and (25) must be limited. A reasonable maximum value fora magnitude of yaw rate Ω can be computed from the following equation(26):

Ω_(dmax) =g/v _(x)  (26)

[0061] where g is acceleration of gravity. The limited value of adesired yaw rate Ω_(dssl) can be computed from the following equation(27): $\begin{matrix}{\Omega_{dssl} = \left\{ \begin{matrix}{\quad \Omega_{dss}} & {{{if}\quad {\Omega_{dss}}} \leq {g/v_{x}}} \\\quad & \quad \\{\left( {g/v_{x}} \right)*{sign}\quad \left( \Omega_{dss} \right)} & {{{if}\quad {\Omega_{dss}}} > {g/v_{x}}}\end{matrix} \right.} & (27)\end{matrix}$

[0062] The limited value of lateral velocity v_(ydssl) can be computedfrom the following equation (28):

v _(ydssl)=[Ω_(dss)/(1−K _(rff))]*{b−M*a*v _(x) ²/(C _(r) *L)+K _(rff)*[a+M*b*v _(x) ²/(C_(f) *L)]}  (28)

[0063] A block 25 receives steady state yaw rate Ω_(dssl) and lateralvelocity V_(ydss). Block 25 represents a desired dynamics of vehicle 10and the delay in the generation of tire lateral forces. In the linearrange of handling, the transfer functions between front steering angleδ_(fdrl) and desired yaw rate Ω_(d) and between front steering angleδ_(fdrl) and desired lateral velocity v_(yd) can be computed by thefollowing equations (29) and (30):

G _(Ω)(s)=Ω_(d)(s)/δ_(fdrl)(s)=(C _(f) /M)*[s−z _(Ω)(v _(x))]/[s²+2*ζ(v_(x))*ω_(n)(v _(x))*s+ω_(n) ²(v_(x))]  (29)

G _(vy)(s)=v _(yd)(s)/δ_(fdrl)(s)=(a*C _(f) /I _(zz))*[s−z _(vy)(v_(x))]/[s²+2*ζ(v _(x) )*ω _(n)(v _(x))*s+ω _(n) ²(v _(x))]  (30)

[0064] In equations (29) and (30), s is the Laplace operand, I_(zz) isthe moment of inertia of vehicle 10 about axis 17, z_(Ω)(v_(x)) andz_(vy)(v_(x)) are zeros of the corresponding transfer functions,ζ(v_(x)) is the damping coefficient, and ω_(n)(v_(x)) is the undampednatural frequency.

[0065] When vehicle 10 has active rear tire steer, the zeros of thetransfer functions depend on feedforward gain K_(rff). Each one of theabove transfer functions can be represented as a product of asteady-state value (corresponding to s=0) and a term representing thedynamics can be computed by the following equations (31) and (32):

G _(Ω)(s)=(Ω_(dss)/δ_(fss))*G _(Ω)′(s)  (31)

G _(vy)(s)=(v _(yss)/δ_(fss))*G _(vy)′(s)  (32)

[0066] Where

G _(ω)′(s)=[−ω_(n) ²(v _(x))/z_(ω)(v _(x)) ]*[s−z _(ω)(v_(x))]/[s²+2*ζ(v _(x))*ω_(n)(v _(x))*s+ω _(n) ²(v _(x))]  (33)

G _(vy)′(s)=[−ω_(n) ²(v _(x))/z _(vy)(v _(x))]*[s−z _(vy)(v _(x))]/[s²+2*ζ(v _(x))*ω_(n)(v _(x))*s+ω _(n) ²(v _(x))]  (34)

[0067] Thus, the dynamic values of the desired yaw rate Ω_(d) andlateral velocity v_(yd) can by obtained by passing the steady statevalues through the differential (or difference) equations (withparameters dependent on speed) representing the dynamics of the transferfunctions G_(Ω)′(s) and G_(vy)′(s).

[0068] In a block 26, the values of desired yaw rate Ω_(d) and side slipvelocity v_(yd) are subsequently passed through first order filtersrepresenting a delay in generating tire forces due to tire relaxationlength. Block 26 can be represented as a transfer function in accordancewith the following equation (35):

G _(f)(s)=a _(f)(v _(x))/[s+a _(f)(v _(x))]  (35)

[0069] in which a filter parameter a_(f)(v_(x)) is speed dependent. Inthe case of vehicle 10 having active rear tire steer, one of the controlobjectives is to achieve quick response of vehicle 10 to steeringinputs. Thus, in this case, the dynamics of vehicle 10 as represented bythe transfer functions (31) and (32) can be ignored, since vehicle 10can respond faster to steering inputs with active rear steer than aconventional vehicle.

[0070] The desired values of yaw rate Ω_(d) and lateral velocity v_(yd)obtained as outputs of block 26 may be subsequently limited in magnitudeby a block 27 depending on the surface conditions. A block 27 canutilize either an explicit estimate of surface coefficient of adhesionin lateral direction μ_(L) or a magnitude of lateral acceleration a_(y).In the first case, a limited value of desired yaw rate Ω_(dl) iscomputed from the 20 following equation (36): $\begin{matrix}{\Omega_{dl} = \left\{ \begin{matrix}{\quad \Omega_{d}} & {{{if}\quad {\Omega_{d}}} \leq {\mu_{L}*{g/v_{x}}}} \\\quad & \quad \\{\left( {\mu_{L}*{g/v_{x}}} \right)*{sign}\quad \left( \Omega_{d} \right)} & {{{if}\quad {\Omega_{d}}} > {\mu_{L}*{g/v_{x}}}}\end{matrix} \right.} & (36)\end{matrix}$

[0071] If the magnitude of lateral acceleration a_(y) is used by block27, the limited desired yaw rate Ω_(dl) is computed from the followingequation (37): $\begin{matrix}{\Omega_{dl} = \left\{ \begin{matrix}{\quad \Omega_{d}} & {{{if}\quad {\Omega_{d}}} \leq {\left( {{a_{y}} + {\Delta \quad a_{y}}} \right)/v_{x}}} \\\quad & \quad \\{\left\lbrack {\left( {{a_{y}} + {\Delta \quad a_{y}}} \right)/v_{x}} \right\rbrack*{sign}\quad \left( \Omega_{d} \right)} & {{{if}\quad {\Omega_{d}}} > {\left( {{a_{y}} + {\Delta \quad a_{y}}} \right)/v_{x}}}\end{matrix} \right.} & (37)\end{matrix}$

[0072] where Δa_(y) is a constant positive value, for example 2 m/s².The magnitude of desired lateral velocity V_(yd) is limited by the valueobtained from equation (26) with the desired yaw rate at steady stateΩ_(dss) replaced by the limited desired yaw rate Ω_(dl).

[0073] Block 27 also outputs a desired side slip angle pd that can becomputed as an arctangent function of the ratio of desired lateralvelocity to longitudinal velocity in accordance with the followingequation (38):

β_(d)=Arctan(v _(yd) /v _(x))  (38)

[0074] Referring to FIG. 5, an embodiment of estimator 30 (FIG. 2) forestimating surface coefficient of adhesion μ_(e) is shown. A block 31performs preliminary calculations. First, it is recognized that the mostrobust signal available is yaw rate Ω, and an entry and an exitconditions are dependent mainly on a yaw rate error, i.e. a differencebetween the desired yaw rate Ω_(dl) and measured yaw rate Ω, and to alesser extent on measured lateral acceleration a_(y) (entry conditiononly). Thus, a yaw rate error is calculated and filtered, and lateralacceleration a_(y) is filtered.

[0075] Second, when vehicle 10 (FIGS. 1A-1D) reaches the limit ofadhesion in a steady turn, a surface coefficient of adhesion can bedetermined as a ratio of the magnitude of a filtered lateralacceleration a_(yfilt) to a maximum lateral acceleration a_(ymax) thatvehicle 10 can sustain on dry pavement as shown in the followingequation (39):

μ_(L)_temp=|a _(yfilt‘|/a) _(ymax)  (39)

[0076] where μ_(L)_temp is a temporary estimate of surface coefficientof adhesion in the lateral direction, and a_(yfilt) is filtered lateralacceleration, which is also corrected for the effects of measuredgravity components resulting from vehicle body roll and bank angle ofthe road.

[0077] A block 32 is designed to recognize situations when vehicle 10operates at or close to the limit of adhesion and estimates a lateralsurface coefficient of adhesion μ_(L) from measured lateral accelerationa_(y). This estimate is calculated by identifying one of the followingthree conditions.

[0078] First, entry conditions are tested during a stage S1. Entryconditions are when vehicle 10 is handling at the limit of adhesion andis not in a quick transient maneuver. Under entry conditions, stage S2sets coefficient of adhesion μ_(L) equal to temporary estimate ofsurface coefficient of adhesion μ_(L)_temp as calculated by equation(37).

[0079] Second, exit conditions are tested during a stage S3. Exitconditions indicate vehicle 10 is well below the limit of adhesion(within the linear range of handling behavior). Under exit conditions, astage S4 resets coefficient of adhesion μ_(L) to a default value of 1.

[0080] Third, when neither the entry conditions nor the exit conditionsare met, a stage S5 holds coefficient of adhesion μ_(L) unchanged from aprevious value (i.e. holding conditions). The only exception is when themagnitude of measured lateral acceleration a_(y) exceeds the maximumvalue predicted using currently held estimate. In this case, stage S5calculates coefficient of adhesion μ_(L) as if vehicle 10 was in anentry condition.

[0081] The entry conditions are met during stage S1 when the followingthree (3) conditions are simultaneously satisfied. The first conditionis either (1) the magnitude of the yaw rate error, that is thedifference between the desired yaw rate Ω_(d) and the measured yaw rateΩ being greater than a threshold as computed in the following equation(40):

|Ω_(d)−Ω|_(filt) >Yaw _(—) Threshold1  (40)

[0082] where the typical value of Yaw_Thershold1 is 0.123 rad/s=7deg/s); or (2) the magnitude of yaw rate error being greater than alower threshold Yaw_Threshold2 for some time Te as computed in thefollowing equation (41):

|Ω_(d)−Ω|_(filt) >Yaw _(—) Threshold2 for Te seconds  (41)

[0083] where Yaw_Threshold2 depends on the magnitude of desired yaw rateΩ_(d) or measured yaw rate Ω. For example, Yaw_Threshold2=4 deg/s+5*|Ω_(d)|=0.07 rad/s+0.09*1|Ω_(d)|, where Ω_(d) is the desired yaw ratein [rad/s]. A typical value of the time period Te for which thiscondition must be satisfied is 0.3 sec. The threshold Yaw_Threshold1used in equation (40) may also depend on the magnitude of desired yawrate Ω_(d) or measured yaw rate Ω.

[0084] The second condition is the signs of the filtered lateralacceleration a_(yfiltl) and the weighted sum of yaw rate Ω and thederivative of yaw rate are the same in accordance with the followingmathematical expression (42):

a _(yfilt1)*(Ω+Yaw _(—) Der _(—) Mult*dΩ/dt)>Sign _(—) Comp  (42)

[0085] where Ω is the measured yaw rate and dΩ/dt is its derivative. Themagnitude of the filtered lateral acceleration a_(yfilt) is limited fromequation (43): $\begin{matrix}{a_{yfiltl} = \left\{ \begin{matrix}{\quad a_{yfiltl}} & {{{if}\quad {a_{yfilt}}} \geq a_{y\quad \min}} \\\quad & \quad \\{a_{y\quad \min}*{sign}\quad \left( \Omega_{d} \right)} & {{{if}\quad {a_{yfilt}}} < a_{y\quad \min}}\end{matrix} \right.} & (43)\end{matrix}$

[0086] where a_(ymin) is a constant with a typical value of 0.2 M/s².Thus if a_(yfilt) is very small in magnitude, it is replaced by thea_(ymin) with a sign the same as the desired yaw rate Ω_(d). This limitis needed to improve estimation on very slick surfaces (e.g. ice) whenthe magnitude of lateral acceleration a_(y) is comparable to the effectof noise, so that the sign of a_(yfilt) cannot be established.

[0087] The recommended values in equation (42) for the constantYaw_Der_Mult is 0.5 and for Sign_Comp is 0.035 (if Ω is in rad/s anddΩ/dt in rad/s²).

[0088] In order to allow lateral acceleration a_(y) to fully build up atthe beginning of maneuver and after each change in sign, before it canbe used for estimation of surface coefficient μ_(L), a condition is usedthat requires both the desired yaw rate Ω_(dl) and lateral accelerationa_(y) to have the same signs for a specific time period (necessary forthe acceleration to build up). In order to keep track of how long thedesired yaw rate Ω_(d) and lateral acceleration a_(y) have had the samesigns, a timer is introduced. In accordance with an equation (44), thetimer becomes zero when the desired yaw rate Ω_(d) and lateralacceleration a_(y) have opposite signs and counts the time that elapsesfrom the moment the signs become and remain the same. $\begin{matrix}{{timer} = \left\{ \begin{matrix}{{0\quad {when}\quad \Omega_{d}*a_{yfiltl}} < {{Ay\_ sign}{\_ comp}}} \\\quad \\{\quad {{timer} + {{loop\_ time}\quad {otherwise}}}}\end{matrix} \right.} & (44)\end{matrix}$

[0089] where Ω_(d) is the desired yaw rate in [rad/s] and Ay_sign_compis a constant with a typical value of 0.2 m/s³.

[0090] The third condition is either (1) the signs of the desired yawrate Ω_(d) and measured lateral acceleration a_(y) are the same and theyhave been the same for some time in accordance with following equation(45):

timer>hold_time  (45)

[0091] The hold_time in equation (42) can be 0.25 s, or (2) themagnitude of a derivative of lateral acceleration da_(y)/dt is less thana threshold in accordance with the following mathematical equation (46):

|da _(y) /dt|<Ay _(—) Der _(—) Thresh  (46)

[0092] A recommended value of the threshold, Ay_Der_Thresh=2.5 m/s³. Thederivative da_(y)/dt is obtained by passing filtered lateralacceleration a_(yfil) through a high pass filter with a transferfunction a_(f)*s/(s+a_(f)) with a typical value of a_(f)=6 rad/s.

[0093] The exit conditions are met during stage S3 when the followingtwo (2) conditions are simultaneously satisfied. The first condition isthe magnitude of yaw rate error filtered is less than or equal to athreshold as illustrated in the following equation (47):

|Ω_(d)−Ω|_(filt) ≦Yaw _(—) Threshold3   (47)

[0094] with a typical value of Yaw_Threshold3=0.10 rad/s.

[0095] The second condition is a low-pass filtered version of themagnitude of the yaw rate error is less than or equal to a threshold asillustrated in the following equation (48):

(|Ω_(d)−Ω|_(filt))_(filt) <Yaw _(—) Treshold4  (48)

[0096] where the value of Yaw_Threshold4=0.06 rad/s is recommended andthe filter is a first order filter with a cutoff frequency of 1.8 rad/s,e.g. a filter with a transfer function a_(f)/(s+a_(f)) with a_(f)=1.8rad/s). The thresholds Yaw_Threshold3 and Yaw_Thereshold4 may depend onthe magnitude of desired yaw rate Ω_(d) or the measured yaw rate Ω.

[0097] A block 33 corrects surface estimate μ_(L) for load transfer.Because of the effects of load transfer to the outside tires duringcornering, which is smaller on slippery surfaces than on dry roads,lateral acceleration a_(y) is not directly proportional to the surfacecoefficient of adhesion μ_(L) To account for this effect, the surfaceestimate μ_(L)_temp computed from equation (37), is corrected using thefollowing equation (49):

μ_(L)=μ_(L)_temp*(c ₁ +C ₂*μ_(L)_temp)  (49)

[0098] where c₁<1 and c₂=1−c₁, so that on dry surfaceμ_(L)=μ_(L)_temp=1, while on slippery surfaces μ_(L)<μ_(L)_temp. Examplevalues are c₁=0.85 and C₂=0.15.

[0099] A block 34 limits surface estimate μ_(L) from below by a valueμ_(Lmin) (a typical value 0.07) and may be limited from above byμ_(Lmax) (a typical value 1.2). Surface estimate μ_(l) can be passedthrough a slew filter, which limits the rate of change of the estimateto a specified value, for example 2/sec, or a low pass filter.

[0100] A block 35 estimates total surface coefficient of adhesion μ_(e)using the following equation (50): $\begin{matrix}{µ_{e} = \left\{ \begin{matrix}\mu_{Lfilt} & {{{when}\quad {a_{xe}}} \leq {Ax\_ Dz}} \\\quad & \quad \\\left\{ {\left( \mu_{Lfilt} \right)^{2} + \left\lbrack {\left( {{a_{xe}} - {Ax\_ DZ}} \right)/a_{x\quad \max}} \right\rbrack^{2}} \right\}^{1/2} & {{{when}\quad {a_{xe}}} > {Ax\_ Dz}}\end{matrix} \right.} & (50)\end{matrix}$

[0101] where Ax_Dz is the dead-zone applied to the estimatedlongitudinal acceleration (a typical value is 2m/s2) and a_(xmax) is amaximum longitudinal deceleration which vehicle 10 can achieve on drysurface (a typical value is 9 m/s²). The square root function in theabove expression can be replaced by a simplified linear equation or by alook-up table. The estimate is finally limited from below by μ_(emin)(typical value is 0.2) and from above by μ_(emax) (1.0).

[0102] The (unfiltered) estimate of surface coefficient in lateraldirection, μ_(L), was found to be good for estimation of vehicle sideslip angle. However, for control purposes, the estimate of the surfacecoefficient in lateral direction may be too low in some situations (forexample during heavy braking on slick surfaces) and may causeunnecessary tight control of slip angle. Therefore, for the purpose ofcontrol the estimated surface coefficient is increased when themagnitude of the estimated vehicle longitudinal acceleration exceedscertain value. Note that separate thresholds on yaw rate error for theentry and exit conditions are used, with the thresholds on the exitconditions being a little tighter.

[0103] Referring to FIG. 6, an embodiment of estimator 30 (FIG. 2) forestimating the actual lateral velocity and slip angle of vehicle 10(FIGS. 1A-1D) as a function of front steering wheel angle signal δ_(f),rear steering wheel angle signal δ_(r), yaw rate signal Ω, estimatedvehicle speed signal v_(x), and the estimated lateral surfacecoefficient of adhesion μ_(L) is shown. The slip angle estimationimplements an iterative nonlinear closed loop observer to determine theestimated vehicle lateral velocity v_(ye) and slip angle β_(e).

[0104] A block 36 of the observer estimates the side slip angles offront axle 11 and rear axle 14 using the following equations (51a) and(51b):

α_(fe) =[v _(ye)(k−1)+a*Ω]/v _(x)−δ_(f)  (51a)

α_(re) =[v _(ye)(k−1)−b*Ω]/v _(x)−δ_(r)  (51b)

[0105] where v_(ye)(k−1) is the estimated lateral velocity from theprevious iteration of the observer, and α_(fe) and α_(re) are theestimated front and rear axle side slip angles, respectively. Thesteering angles δ_(f) and δ_(r) are the actual (measured) steeringangles of front tires 12 and 13, and rear tires 15 and 16, respectively,including the corrective terms.

[0106] A block 37 of the observer estimates lateral forces F_(yfe) ofthe front axle 11 according to one of two functions as illustrated inthe following equation (52): $\begin{matrix}{F_{yfe} = \left\{ \begin{matrix}{\quad {{{- C_{f}}*\alpha_{fe}*\left( {1 - \left( {b_{cf}*\left( {{\alpha_{fe}}/\mu_{L}} \right)} \right)} \right)},}} & {{{if}\quad {\alpha_{fe}}} < {\mu_{L}*\alpha_{f^{*}}}} \\\quad & \quad \\{{- N_{f^{*}}}*\left( {{\alpha_{fe}}/\alpha_{fe}} \right)*\left\lbrack {\mu_{L} + {s_{f}*\left( {{{\alpha_{fe}}/\alpha_{f^{*}}} - \mu_{L}} \right)}} \right\rbrack} & {{{if}\quad {\alpha_{fe}}} \geq {\mu_{L}*\alpha_{f^{*}}}}\end{matrix} \right.} & (52)\end{matrix}$

[0107] where s_(f) is a small non-negative number (the slope of theF_(yf)−α_(f) curve at the limit of adhesion), e.g., s_(f)=0.05, andwhere α_(f*) is defined by the following equation (53):

α_(f*)=1/(2*b _(cf),)  (53)

[0108] where b_(cf) is defined by the following equation (54):

b _(cf) =C _(f)/(4*N _(f)),  (54)

[0109] where N_(f) is defined by the following equation (55):

N _(f*) =M*b*(a _(ymax)+Δ_(a))/(a+b)  (55)

[0110] where a_(ymax) is the maximum lateral acceleration that vehicle10 can sustain on a dry surface in m/s² and Δ_(a) is a positiveconstant, e.g., Δ_(a)=0.5 m/s². M is the nominal value of the totalvehicle mass.

[0111] The observer similarly estimates lateral forces F_(yre) of therear axle 14 according to the following equation (56): $\begin{matrix}{F_{yre} = \left\{ \begin{matrix}{\quad {{{- C_{r}}*\alpha_{re}*\left( {1 - {b_{cr}*{\alpha_{re}}}} \right)},}} & {{{if}\quad {\alpha_{re}}} < {\mu_{L}*\alpha_{r^{*}}}} \\\quad & \quad \\{{- N_{r^{*}}}*\left( {{\alpha_{re}}/\alpha_{re}} \right)*\left\lbrack {\mu_{L} + {s_{r}*\left( {{{\alpha_{re}}/\alpha_{r^{*}}} - \mu_{L}} \right)}} \right\rbrack} & {{{if}\quad {\alpha_{re}}} \geq {\mu_{L}*\alpha_{r^{*}}}}\end{matrix} \right.} & (56)\end{matrix}$

[0112] where s_(r) is a small non-negative number, e.g., s_(r)=0.05 andwhere α_(r*) is defined by the following equation (57):

α_(r*)=1/(2*b _(cr),)  (57)

[0113] where b_(cr) is defined by the following equation (58):

b _(cr) =C _(r)/(4*N _(r*)),  (58)

[0114] where N_(r*) is defined by the following equation (59):

N _(r*) =M*a*(a _(ymax)+Δ_(a))/(a+b).  (59)

[0115] A block 38 of the observer then estimates a state variable q(k)related to lateral velocity according to the following equation (60):

q(k)=q(k−1)+Δt*{−(1+g ₂)*v _(x)*Ω+((1+g ₃)/M−a*g ₁ /I _(zz))*F_(yfe)+[(1+g ₃)/M+b*g ₁ /I _(zz) ]*F _(yre)+(g ₂ −g ₃)*a _(y) −g ₄ *ΔA_(yf)}  (60)

[0116] where ΔA_(y) is defined by the following equation (61):

ΔA _(y) =a _(y)−(F _(yfe) +F _(yre))/M,  (61)

[0117] and ΔA_(yf) is ΔA_(y) passed through a first order digital lowpass filter, for example, with a cut off frequency of 1 rad/s.

[0118] A block 39 of the observer uses state variable q(k) to determineestimates of lateral velocity v_(ye) and slip angle β_(e) usingequations (62) and (63):

v _(ye)(k)=[q(k)+g ₁*•_(a)]/(1+g ₂)  (62)

β_(e)=Arctan[v _(ye)(k)/v _(x)].  (63)

[0119] The gains g₁, g₂, g₃ and g₄ are tuning parameters preset by asystem designer, typically through experimentation on a test vehicle,and may vary from implementation to implementation. The estimatedlateral velocity v_(ye) and the estimated slip angle β_(e) are the mainoutputs of the observer.

[0120] Referring to FIG. 7, one embodiment of controller 40 inaccordance with the present invention is shown. In controller 40, anoverall corrective yaw moment is determined and expressed in terms of adesired speed differential signal Δv_(lr3t) (which is achieved bydifferential braking) between either front tire 12 and front tire 13(FIGS. 1A-1D), or rear tire 15 and rear tire 16 (FIGS. 1A-1D). Thecorrective yaw moment is also expressed in terms of a summation of frontsteer angle correction signal Δδ_(f) and front steering angle signalδ_(fdr1) (FIG. 2) to form the total front steering angle signal δ_(ftd)and in terms of a summation of rear steer angle correction signal Δδ_(r)and rear steering angle signal δ_(rff) (FIG. 2) to form the totaldesired rear steer angle signal δ_(rtd). The magnitudes of total desiredrear steer angle signal δ_(rtd) and the total desired front steeringangle signal δ_(ftd) may be subsequently limited to desired rearsteering angle signal δ_(rtd1) and desired front steering angle signalδ_(ftd1), respectively.

[0121] A block 41 calculates desired speed differential signal Δv_(lr3),front steer angle correction signal Δδ_(f) and rear steer anglecorrection signal Δδ_(r). The corrective yaw moment is obtained by afeedback control operating on the yaw rate error and the side slipvelocity (or side slip angle) error. The yaw rate error Ω_(d)−Ω is thedifference between the desired yaw rate signal Ω_(d) and measured yawrate signal Ω. Similarly, the side slip velocity error is the differencebetween the desired side slip velocity signal v_(yd) and the estimatedside slip velocity signal v_(ye). The control law is essentially a PD(proportional and derivative) feedback control law, in which the controlgains depend on vehicle speed signal v_(x), estimated surfacecoefficient of adhesion signal μ_(e), and on the magnitude of theestimated vehicle slip angle error. Thus, for the delta velocity signalΔv_(lr3), the control law equation (64) may be written as follows:$\begin{matrix}{{\Delta \quad v_{lr3}} = {{{k_{\Omega \quad p}\left( {v_{x},\mu_{e}} \right)}*\left( {\Omega_{d} - \Omega} \right)} + {{k_{\Omega \quad d}\left( {v_{x},\mu_{e}} \right)}*{{d\left( {\Omega_{d} - \Omega} \right)}/{dt}}} + {{k_{vyp}\left( {v_{x},\mu_{e},{{\beta_{d} - \beta_{e}}}} \right)}*\left( {v_{yd} - v_{ye}} \right)} + {{k_{vyd}\left( {v_{x},\mu_{e},{{\beta_{d} - \beta_{e}}}} \right)}*{{d\left( {v_{yd} - v_{ye}} \right)}/{dt}}}}} & (64)\end{matrix}$

[0122] where k_(Ωp)(v_(x),μ_(e)) and k_(Ωd)(v_(x),μ_(e)) are theproportional and derivative yaw rate gains, while k_(vyp)(v_(x),μ_(e),|β_(d)−β_(e)|) and k_(vyd)(V_(x), μ_(e), |μ_(d)−μ_(e)|) are theproportional and derivative lateral velocity gains. The magnitudes ofthe gains for each velocity and surface coefficient are tuned throughvehicle testing and are implemented as look up tables. Typically, theproportional yaw rate gain k_(Ωp)(v_(x),μ_(e)) and derivative yaw rategain k_(Ωd)(v_(x), μ_(e)) increase nearly proportionally with vehiclespeed v_(x) and decrease as the estimated surface coefficient ofadhesion μ_(e) increases. The lateral velocity gains,k_(vyp)(v_(x),μ_(e), |β_(d)−β_(e)|) and k_(vyd)(v_(x),μ_(e),|β_(d)−β_(e)|), increase with vehicle speed and increase quite rapidlyon slippery surfaces. This is done to provide a proper balance betweenyaw control and side slip control. On dry surfaces, the yaw ratefeedback control usually dominates to achieve responsive handling, whileon slippery surface the control of side slip increases to achieve betterstability. In addition, the slip angle gains may depend on the magnitudeof side slip angle error, with the gain generally increasing as the sideslip angle error increases. For example, the gain may be zero or closeto zero when the magnitude of side slip angle error is below athreshold, and increases as the side slip angle error increases inmagnitude.

[0123] There exist several modifications of the control law, which maybe considered the special cases of the control law (64). First, thedesired side slip velocity and side slip angle may be set to zero. Inthis case, the last two terms in equation (64) are proportional andderivative terms with respect to side slip velocity, rather than sideslip errors. In this case, the desired side slip velocity does not needto be computed, which simplifies the algorithm. This simplification isjustified, because at higher speeds the desired side slip angles aresmall, especially for active rear steer vehicles. Further simplificationmay be achieved by deleting the third term in the control law (64),involving the side slip velocity. In this case, the control law includesP (proportional) and D (derivative) yaw rate terms, but only aderivative lateral velocity term. In that manner, the estimation ofvehicle side slip velocity is avoided and the algorithm is furthersimplified. The control gains may depend on whether vehicle is inoversteer or understeer condition.

[0124] As discussed earlier, differential speed signal Δv_(lr3)determined for the brake controller can be converted into equivalentsteering angle correction signal Δδ_(r) for rear axle 14 and frontsteering angle correction signal Δδ_(f) for axle 12. Thus the feedbackportions of the front or rear steering angles can be computed fromequations (65) and (66):

Δδ_(r) =g _(f)(v _(x), μ_(e))*Δv _(lr3)  (65)

Δδ_(f) =g _(r)(v _(x), μ_(e))*Δv _(lr3)  (66)

[0125] where the gains can vary with speed and the estimated surfacecoefficient of adhesion.

[0126] Block 42 determines a vehicle steer flag, which determineswhether vehicle 10 is in understeer (flag=1) or oversteer (flag=0). Thefollowing is an example of steer flag determination.

[0127] Vehicle 10 is in understeer if either front steering angle signalδ_(f), control signal Δv_(lr3) and lateral acceleration signal a_(y) areall in the same direction or when vehicle 10 is plowing on a slipperysurface. Vehicle 10 is in oversteer if either front steering anglesignal δ_(f) is in different direction from control signal Δv_(lr3); orfront steering angle signal δ_(f) and control signal Δv_(lr3) are in thesame direction, but lateral acceleration signal a_(y) is in oppositedirection. If neither oversteer nor understeer conditions are satisfied,previous steer definition is held. It is theoretically possible thatvehicle 10 is plowing (understeer) and front steering angle signal δ_(f)and control signal Δv_(lr3) have opposite signs (oversteer). In thiscase vehicle state is considered oversteer (i.e. oversteer overridesundersteer if both are true).

[0128] The situation when vehicle 10 is plowing is identified when themagnitude of the desired yaw rate Ω_(d) is significantly larger than themagnitude of measured yaw rate Ω over a pre-defined period of time, andthe measured yaw rate Ω is small. This can happen only on very slipperyroad surface. In this situation, we do not demand that front steeringangle signal δ_(f), control signal Δv_(lr3) and lateral accelerationsignal a_(y) have the same signs, in order to declare understeer, sincelateral acceleration signal a_(y) may be very small in magnitude.

[0129] The over/understeer flag is used to further influence the controlactions. If the brake control system is a four channel system, i.e. itcan actively apply brakes to either front tires 12 and 13 (FIGS. 1A-1D)or rear tires 15 and 16 (FIGS. 1A-1D), then the control command Δv_(lr3)is applied to tire 12 and/or tire 13 when vehicle 10 is in oversteer andto tire 15 and./or tire 16 when vehicle 10 is in understeer. For a twochannel system, the control command Δv_(lr3) is always applied to tire12 and/or tire 13. The actual commanded differential speed signalΔv_(lr3) is corrected for the difference in tire velocities, resultingfrom kinematics of turn. During cornering maneuvers, free rolling tireshave a speed difference equal to the product of vehicle yaw rate Ω, andthe track width t_(w). Thus, the target tire slip difference can becomputed from equation (67):

Δv _(lr3t) =Δv _(lr3) +t _(w)*Ω  (67)

[0130] When the driver is not braking, the velocity difference betweenfront tires 12 and 13 is achieved by braking of one or both front tires12 and 13, and the velocity difference between rear tires 15 and 16 isachieved by braking of one or both front tires 15 and 16. When driver isbraking, the braking force may also be reduced on the opposite side, ifbraking of the desired tire reached a saturation point without achievingthe desired speed difference.

[0131] A block 43 tests entry and exits conditions for applying thebrake command Δv_(lr3t) to vehicle 10. The brake command Δv_(lr3t) isapplied only if entry conditions for the active brake control areestablished and only until the exit conditions for active brake controlsatisfied. First, the estimated vehicle speed signal v_(x) must be abovea certain entry speed v_(min), which is rather low, for example 5 mph.If this condition is satisfied, then the brake system becomes activewhen the magnitude of yaw rate error exceeds a threshold value, whichdepends on vehicle speed signal v_(x), front steering angle signal δ_(f)and over or understeer flag. The yaw rate error consists of aproportional and a derivative terms. Thus the entry condition can becomputed from the following equation (68):

|Ω_(d) −Ω+k _(e) *d(Ω_(d)−Ω)/dt |>Ω _(thresh)(v_(x), δ_(f) ,steer_flag)  (68)

[0132] where k_(e) is a constant and Ω_(thresh)(v_(x), δ_(f),steer_flag) is a threshold, which depends on the vehicle speed signalv_(x), front steering angle signal δ_(f) and steer flag. It is larger inundersteer condition than in oversteer. The entry conditions for thebrake system are significantly relaxed, or even the system may not beallow to enter, when vehicle 10 is being braked in ABS mode. In thiscase, the directional control is provided by steering only, until theerrors in yaw following are quite large. In the case of braking on splitmu surface (a surface with significantly different coefficients ofadhesion under left and right tires) the entire correction of the yawmotion is provided by steering alone. This is done in order to avoidcompromising the stopping distance.

[0133] An exit condition is established if the magnitude of the yaw rateerror, as defined above, is below a predetermined yaw rate errorthreshold (which is lower than the entry threshold) for a specifiedperiod of time or when vehicle speed drops below a certain value.

[0134] When entry conditions are not met, the active brake controlsystem is disabled. During this time vehicle dynamic behavior iscontrolled through active steer control, front or rear, which do nothave entry conditions. A block 44 determines total commanded targetedcontrol valves. First, rear steering angle δ_(rtd) is computed as thesum of the feedforward part δ_(rff) and the feedback part Δδ_(r) inaccordance with the following equation (69):

δ_(rtd)=δ_(rff)+Δδ_(r)  (69)

[0135] If vehicle 10 is in oversteer, the commanded rear steer angle islimited in order to limit the side slip angle of the rear tires to amaximum value α_(rmax)(μ_(e)), which depends on the estimated surfacecoefficient of adhesion (it decreases when the surface estimatedecreases). Typical shapes of the curves relating lateral force to thetire slip angle for two different surfaces are shown in FIG. 8.Increasing slip angle beyond α_(rmax) leads to decline in the magnitudeof lateral force on most surfaces. The purpose is to avoid increasingslip angle beyond that corresponding to the peak lateral force. Thisyields the following equation (70): $\begin{matrix}{\delta_{rtdl} = \left\{ \begin{matrix}{{\left( {v_{ye} - {b*\Omega}} \right)/v_{x}} - \alpha_{r\quad \max}} & {{{if}\quad \delta_{rtd}} < {{\left( {v_{ye} - {b*\Omega}} \right)/v_{x}} - \alpha_{r\quad \max}}} \\{{\left( {v_{ye} - {b*\Omega}} \right)/v_{x}} + \alpha_{r\quad \max}} & {{{if}\quad \delta_{rtd}} > {{\left( {v_{ye} - {b*\Omega}} \right)/v_{x}} + \alpha_{r\quad \max}}} \\{\quad \delta_{rtd}} & {otherwise}\end{matrix} \right.} & (70)\end{matrix}$

[0136] Similarly, the commanded front steer angle correction, Δδ_(ftd)consists of the feedforward part δ_(fff) and the feedback part Δδ_(f) inaccordance with following equation (71):

Δδ_(ftd)=δ_(fff)+Δδ_(f)  (71)

[0137] The total desired steering angle δ_(ftd) is the sum of thesteering angle correction and the angle commanded by the driver δ_(fdr)as computed from the following equation (72):

δ_(ftd)=δ_(fdr)+Δδ_(ftd)  (72)

[0138] This steering may subsequently be a subject of the followinglimitation. If vehicle is in an understeer condition, then the totalfront tire steering angle δ_(ftd) is limited to by the followingequation (73): $\begin{matrix}{\delta_{ftd1} = \left\{ \begin{matrix}{{\left( {v_{ye} + {a*\Omega}} \right)/v_{x}} - \alpha_{f\quad \max}} & {{{if}\quad \delta_{ftd}} < {{\left( {v_{ye} + {a*\Omega}} \right)/v_{x}} - \alpha_{f\quad \max}}} \\{{\left( {v_{ye} + {a*\Omega}} \right)/v_{x}} + \alpha_{f\quad \max}} & {{{if}\quad \delta_{ftd}} > {{\left( {v_{ye} + {a*\Omega}} \right)/v_{x}} - \alpha_{f\quad \max}}} \\\delta_{ftd} & {otherwise}\end{matrix} \right.} & (73)\end{matrix}$

[0139] where α_(fmax)(μ_(e)) is a front tires slip angle correspondingto maximum lateral force. It is a function of the estimated surfacecoefficient of adhesion μ_(e).

[0140] Thus, during normal vehicle operation, vehicle 10 is controlledthrough steering inputs only, which are quite effective in controllingvehicle yaw motion in and close to the linear range of handlingbehavior. Only if the actual response of vehicle 10 significantlydeviates from the desired response, the active brake control isactivated in addition to the steering control.

[0141] While the embodiments of the present invention disclosed hereinare presently considered to be preferred, various changes andmodifications can be made without departing from the spirit and scope ofthe invention. The scope of the invention is indicated in the appendedclaims, and all changes that come within the meaning and range ofequivalents are intended to be embraced therein.

1. An integrated active steering and braking control method for avehicle, the vehicle including an axle, a first tire, a second tire, asteering system, and a braking system, said method comprising:determining a first corrective yaw moment as a function of a steeringangle of the axle; determining a second corrective yaw moment as afunction of a speed differential between the first tire and the secondtire; providing a corrective steering signal to the steering systemwhereby said first corrective yaw moment is applied to the vehicle; andproviding a corrective braking signal to the braking system whereby saidsecond corrective yaw moment is applied to the vehicle.
 2. The method ofclaim 1, wherein said corrective steering signal and said correctivebraking signal are concurrently provided whereby said first correctiveyaw moment and said second corrective yaw moment are concurrentlyapplied to the vehicle.
 3. An integrated active steering and brakingcontrol method for a vehicle, the vehicle including an axle, a firsttire, and a second tire, said method comprising: determining a desiredspeed differential between the speed of the first tire and the speed ofthe second tire; and determining a desired steering angle of the axle asa function of said desired speed differential.
 4. The method of claim 3,further comprising: determining a corrective braking signal as afunction of said desired speed differential.
 5. The method of claim 3,further comprising: determining a corrective steering signal as afunction of said desired steering angle.
 6. The method of claim 3,further comprising: applying a limitation to said desired steeringangle; and determining a corrective steering signal as a function ofsaid desired steering angle in view of said limitation.
 7. The method ofclaim 3, further comprising: selectively determining a correctivebraking signal as a function of said desired speed differential; anddetermining a corrective steering signal as a function of said desiredsteering angle.
 8. An integrated active steering and braking controlmethod for a vehicle, the vehicle including an axle, a first tire, and asecond tire, said method comprising: receiving a plurality ofoperational signals indicative of an operational state of the vehicle;determining a feedforward portion of a corrective front steering anglesignal in response to said plurality of operational signals; anddetermining a feedforward portion of a corrective rear steering anglesignal in response to said plurality of operational signals.
 9. Themethod of claim 8, further comprising: determining a desired yaw rate inresponse to said plurality of operational signals; determining a desiredside slip velocity in response to said plurality of operational signals;and determining a desired side slip angle in response to said pluralityof operational signals.
 10. The method of claim 8, further comprising:estimating a surface coefficient of adhesion in response to saidplurality of operational signals estimating a side slip velocity inresponse to said plurality of operational signals; and estimating a sideslip angle in response to said plurality of operational signals.
 11. Themethod of claim 8, further comprising: determining a feedback portion ofsaid corrective front steering angle signal in response to saidplurality of operational signals; and determining a feedback portion ofsaid corrective rear steering angle signal in response to said pluralityof operational signals.
 12. An integrated active steering and brakingcontrol method for a vehicle including an axle, a first tire, a secondtire, a steering system, and a braking system, said method comprising: afirst controller operable to determine a first corrective yaw moment asa function of a steering angle of the axle and to determine a secondcorrective yaw moment for the vehicle as a function of a speeddifferential between the first tire and the second tire; and a secondcontroller operable to provide a corrective steering signal to thesteering system whereby said first corrective yaw moment is applied tothe vehicle, and to provide a corrective braking signal to the brakingsystem whereby said second corrective yaw moment is applied to thevehicle.
 13. The system of claim 12, wherein said second controller isoperable to concurrently provide said corrective steering signal to thesteering system and said corrective braking signal to the braking systemwhereby said first corrective yaw moment and said second corrective yawmoment are concurrently applied to the vehicle.
 14. A vehicle,comprising: an axle; a first tire; a second tire; and an integratedactive steering and braking control system operable to determine adesired speed differential between a speed of said first tire and aspeed of said second tire and to determine a desired steering angle ofsaid axle as a function of said desired speed differential.
 15. Thevehicle of claim 14, wherein said system is further operable todetermine a corrective braking signal as a function of said desiredspeed differential.
 16. The vehicle of claim 14, wherein said system isfurther operable to determine a corrective steering signal as a functionof said desired steering angle.
 17. The vehicle of claim 14, whereinsaid system is further operable to apply a limitation to said desiredsteering angle and to determine a corrective steering signal as afunction of said desired steering angle in view of said limitation. 18.The vehicle of claim 14, wherein said system is further operable toselectively determine a corrective braking signal as a function of saiddesired speed differential and to determine a corrective steering signalas a function of said desired steering angle.
 19. An integrated activesteering and braking control system for a vehicle, comprising: a meansfor determining a feedforward portion of a corrective front steeringangle signal in response to a plurality of operational signalsindicative of an operational state of the vehicle; and a means fordetermining a feedforward portion of a corrective rear steering anglesignal in response to said plurality of operational signals.
 20. Thesystem of claim 19, further comprising: a means for determining adesired yaw rate in response to said plurality of operational signals; ameans for determining a desired side slip velocity in response to saidplurality of operational signals; and a means for determining a desiredside slip angle in response to said plurality of operational signals.21. The system of claim 19, further comprising: a means for estimating asurface coefficient of adhesion in response to said plurality ofoperational signals a means for estimating a side slip velocity inresponse to said plurality of operational signals; and a means forestimating a side slip angle in response to said plurality ofoperational signals.
 22. The system of claim 8, further comprising: ameans for determining a feedback portion of said corrective frontsteering angle signal in response to said plurality of operationalsignals; and a means for determining a feedback portion of saidcorrective rear steering angle signal in response to said plurality ofoperational signals.